Sounds like your 6600 is just fine to me.There are poppet valves in the hydraulic system that do not let the system operate until the engine is running at higher rpm's.I was told one time it is a safety thing.

I would suspect that the main relief valve on the main hydraulic valve is blocked or plugged. The relief valve is located under the operator platform and is the valve that controls header lift and variable ground speed etc. It has a pressure number stamped on a plug usually 2000 psi or 2200 psi. Remove it and have someone test it. We had a pump blow the side out and this was the problem. Hope this helps

Maybe...your engine powershaft is bent or has a bearing going bad. This would put a lot of vibration on the pump shaft. Is the torque arm brokenIJIJ or the rubber strap holding the torque arm brokenIJIJ Just a couple of things to look at. Hope this helps.